Question: What is the value of the following logarithm? $\log_{512} 8$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $8$ is the cube root of $512$ That is, $\sqrt[3]{512} = 512^{1/3} = 8$ Thus, $\log_{512} 8 = \dfrac{1}{3}$.